On the first sign change of Fourier coefficients of cusp forms at sum of two squares
type: Item
instance of: scholarly article
title: On the first sign change of Fourier coefficients of cusp forms at sum of two squares
zbMATH Open document ID: 1479.11065
author: Manish K. Pandey
author: Prashant Tiwari
published in: Research in Number Theory
publication date: 2021-10-20T00:00:00Z
review text: Since Fourier coefficients of modular forms carry a lot of arithmetic information, several problems about them are being studied. One of them is certainly the sign change problem. There are many papers about sign change problem with different settings. In the paper under review, the authors consider the problem of first sign change of Fourier coefficients of a primitive cusp form at a sparse sequence, where elements of the sparse sequence can be written as a sum of two squares. As a main result, they give an effective upper bound on elements of such a sparse sequence to have first sign change. The main tool is coming from \textit{W. Kohnen} and \textit{J. Sengupta}'s work [Math. Z. 254, No. 1, 173--184 (2006; Zbl 1220.11060)] based on analytic number theory calculations.
reviewed by: İlker İnam
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11M06
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 7411930
zbMATH Keywords: cusp form
zbMATH Keywords: Fourier coefficients
zbMATH Keywords: sign change
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Rankin-Selberg \(L\)-function
MaRDI profile type: Publication
full work available at URL: s40993-021-00291-9
OpenAlex ID: W3202352443
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DOI: 10.1007/S40993-021-00291-9
description: scientific article